Document EP 270,515 describes linear copolymers of general formula S.sub.1 -B.sub.1 -B.sub.2 /S.sub.2 -S.sub.3 containing from 60 to 95% of vinylaromatic compound and from 5 to 40% of diene. In the formula, S.sub.1 and S.sub.3 are vinylaromatic polymer blocks, B.sub.1 is a polydiene block and B.sub.2 /S.sub.2 is a statistical block copolymer of conjugated diene and of vinylaromatic monomers. This copolymer has satisfactory mechanical properties but its optical properties are relatively mediocre since the haze index for the pure resin scarcely falls below 6.7 whereas it scarcely falls below 13.5 when it is mixed with crystal polystyrene.
Document U.S. Pat. No. 4,221,884 describes bimodal star block copolymers, which are particularly resilient at low temperatures, of general formula (S.sub.1 -S.sub.2 /B.sub.1 -B.sub.2).sub.m -X-(B.sub.2 S.sub.2 / B.sub.1 ).sub.n. In this formula, S.sub.1 is a non-elastomeric block, S.sub.2 /B.sub. is a copolymer block of a vinylaromatic compound and of a conjugated diene. In this copolymer, the ratio by mass of S.sub.2 to B.sub.1 is less than 1. B.sub.2 is a conjugated polydiene block containing 20 to 40% by weight of all the conjugated diene contained in the star block copolymer. These copolymers have mediocre transparencies and are difficult to mix with crystal polystyrene.
Document U.S. Pat. No. 4,925,899 describes bimodal star block copolymers containing from 60 to 90% by weight of a vinylaromatic monomer and from 40 to 10% by weight of a conjugated diene. This copolymer is represented by the general formula (S.sub.1 -S.sub.2 -B.sub.1 /S.sub.3 -B.sub.2).sub.m -X-(B.sub.2 -S.sub.3 /B.sub.1 -S.sub.2).sub.n in which S.sub.1 and S.sub.2 are vinylaromatic polymer blocks, B.sub.2 is a conjugated polydiene block containing up to 20% of all the diene units of the copolymer and B.sub.1 /S.sub.3 and S.sub.3 /B.sub.1 are copolymer blocks of a vinylaromatic monomer and of a conjugated diene, the said copolymer blocks consisting of diene B.sub.1 and of vinylaromatic monomer S.sub.3 with a B.sub.1 :S.sub.3 ratio by mass of between 0.8 and 1.2 resulting from vinylaromatic monomer. However, these copolymers have such high melt indices that it is difficult to envisage mixing them with crystal polystyrene.